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On super and restricted connectivity of some interconnection networks. (English) Zbl 1240.05177
Summary: The super connectivity (super edge-connectivity) of a connected graph is the minimum cardinality of a vertex-cut (edge-cut) whose removal does not isolate a vertex. In this paper we consider the two parameters for a special class of graphs $G(G_0,G_1;M)$, proposed by Chen et al. [{\it Y.-C. Chen}, {\it J.J.M. Tan}, {\it L.-H. Hsu}, and {\it S.-S. Kao}, “Super-connectivity and super-edge-connectivity for some interconnection networks,” Appl. Math. Comput. 140, No. 2--3, 245--254 (2003; Zbl 1025.05037)], obtained from two $k$-regular $k$-connected graphs $G_0$ and $G_1$ with the same order by adding a perfect matching between their vertices. Our results improve those of Chen et al. [loc.cit.]. As applications, the super connectivity and the super edge-connectivity of the $n$-dimensional hypercube, twisted cube, cross cube, Möbius cube and locally twisted cube are all $2n-2$.

##### MSC:
 05C40 Connectivity 94C15 Applications of graph theory to circuits and networks